Use this dynamic worksheet to answer the questions that follow and determine the equation for the area of any parallelogram.
1. Let's start by clicking on the "Show variables" check box. Since we're going to derive the formula, let's make sure we're using the same terms. No other variables should be part of the equation you derive. When you're done, uncheck the "Show variables" check box.
2. Slide the Height slider bar until the figure is two units tall.
3. Click on the "Show dimensions" check box to display the sizes of the base and height. Can you determine the area of the parallelogram?
4. Use the Slide bar to slide part of the parallelogram all the way to the right. Now can you see how to determine the area? Remember how you determined the area of a rectangle.
5. If you don't remember, click on the "Show unit square" check box to reveal a unit square. Use it to count the number of squares in the figure.
6. The number of squares within the figure is the area of the figure. Click on the check box to "Show area." The area should be the same as the number of squares you counted. If not, count them again.
7. What do you think will happen when you slide the Height slider bar to change the number of rows? Why? Test your conjecture.
8. Experiment by doing the following several times:
a) uncheck the "Show area" check box;
b) move the Height slider bar;
c) calculate the area on your own using the variables "b" for base and "h" for height -- click on the "Show dimensions" check box for a quick count of base and height;
d) check the "Show area" check box to verify.
e) click on the reset button in the upper right hand corner to reset this construction before repeating.
9. When you are satisfied, write down the equation for area in terms of base and height. Check your answer by checking the "Show equation" check box. If you have difficulty, raise your hand so your teacher can help.
Take the quiz!
Go to: Rhombus, Trapezoid, or
Quadrilateral Test Site Map
Worksheet created by T. Gastauer, Created with GeoGebra